If you use I2C LCD displays and DS18B20 temperature sensors you're fine, else you may run out of pins, depending on what "a couple of" is actually in numbers. Standard LCDs with 4-bit parallel interface use at least 6 pins, thermistors use an analog pin, so you need 14 pin out of 20 just for them. Usually you want the serial interface for debugging, make 2 additional pins, leaving 4 for your relays. Is this a couple of?
I am looking to display 2 different LCD's, use 2 different temp sensors, and run a couple relays for power outlets. Will the Arduino be sufficient for this setup?
which I have not purchased yet.